Numerical Simulation Of Unsteady Underground Water Filtration In A Porous Medium

Аннотация

The problem of the process of unsteady underground water filtration in a porous medium considered in the paper is an urgent one. It is related to design and development of hydraulic structures, regulation of groundwater runoff, flooding, salinization and waterlogging; all these cause great damage to the national economy. For the development of a mathematical model of the process, the research associated with this problem is analyzed in detail in this paper and a mathematical apparatus for studying and predicting changes in the groundwater level during the process of filtering in porous media is proposed. To construct a mathematical model of the process, Darcy’s law is used and the source of infiltration (rain, watering) and evaporation is taken into account. The task in the study is considered at various boundary and internal conditions. Since the process is described by a nonlinear differential equation in partial derivatives, an analytical solution is difficult to obtain. To solve it a numerical algorithm based on a finite-difference scheme has been developed; an iterative scheme is used for nonlinear terms, its convergence is checked. Various locally-one-dimensional schemes were constructed for solving boundary problems of filtering in simply connected and multiply connected regions.